Question

100°
9
10
u
t
8
9² = 8² + 10² - 2(8)(10)cos(100°)
9 = 8 + 10 - 2(8)(10)cos(100°)
10² = 8² + 100 - 2(8)(10)cos(100°)
8² = 9² + 10² - 2(9)(10)cos(100°)

Explanation:

Step1: Recall the Law of Cosines

The Law of Cosines for a triangle with sides \(a\), \(b\), \(c\) and the angle \(\theta\) opposite to side \(c\) is \(c^{2}=a^{2}+b^{2}-2ab\cos\theta\). In the given triangle, if we consider the side of length \(s\) as \(c\), the sides of lengths \(9\) and \(10\) as \(a\) and \(b\) respectively, and the included - angle \(100^{\circ}\) as \(\theta\).

Step2: Apply the Law of Cosines

We get \(s^{2}=9^{2}+10^{2}-2(9)(10)\cos(100^{\circ})\).

Answer:

\(s^{2}=9^{2}+10^{2}-2(9)(10)\cos(100^{\circ})\)